Numerical Data Can Be Broken Down Into Two Different Types

Mr. J GallagherYear 7 Mathematics

Statistics

Name: ______

Types of Data:

Numerical data is data that can be answered with numbers. For example when you are asked how many students are in your class or how many bedrooms in your house.

Numerical data can be broken down into two different types:

Discrete numerical data is data that has a finite ending or can be counted. By definition, it can only be certain values. For example, the number of pencils in a box represents discrete data.

Continuous numerical data, on the other hand, represents values with infinite possibilities, such as the weight of an object or the measurement of rainfall. Could be an infinite number of decimals.

Categorical data is data that cannot be answered with numbers. For example when you are asked what colour are your eyes or what is your favourite soccer team.

Categorical data can be broken down into two different categories:

Ordinal categorical data can be ordered in some way. For example, your exam grades (A, B, C, D, E, F, NG) or your social class (Lower, Middles, Upper).

Nominal categorical data cannot be ordered. For example, your hair colour or your phone type.

Question 1

State whether the following questions are Numerical or Categorical:
- How many books are in your schoolbag?

- What colour is your hair?

- How many people live in Abu Dhabi?

- What is your favourite subject?

Question 2(L2)

State whether the following questions are Discrete or Continuous:
- How much rain fell in Abu Dhabi in 2017?

- How many students are in this class?

- What height are you?

- What distance is it from Abu Dhabi to Dubai?

Question 3(L2)

State whether the following questions are Ordinal or Nominal:
- What grade did you receive in your last maths assessment? (A,B,C,D,….)

- What type of car do you drive?

- What subjects do you study?

- What country are you from?

Question 4(L3)

Gerry is carrying out a survey on the students in his class. His questions are about the social media apps which the students use.

Write a question (*or 2) that Gerry could use that would give

- Discrete Numerical Data

- Continuous Numerical Data

- Nominal Categorical Data

- Ordinal Categorical Data

Frequency Tables: A simple way to convey information

Car Game 1

Green / Blue / Red / Yellow
Tally
Frequency

** What is the modal (mode) car?

Car Game 2

Green / Blue / Red / Yellow
Tally
Frequency

** What is the modal (mode) car?

Car Game 3

Green / Blue / Red / Yellow
Tally
Frequency

What is the modal (mode) car?

Car Game 4

Green / Blue / Red / Yellow
Tally
Frequency

What is the modal (mode) car?

Object Game

Write down the items that you remember.

How many did you remember?

Frequency Table

Objects Remembered / Tally / Frequency
0
1
2
3
4
5
6
7
8
9
10

Line Plots

Use the graphs provided to answer each of the following questions:

Question 1

On what day were the most cars sold?

How many cars were sold in total?

What percentage of cars were sold
on Saturday? (L2)

Question 2

What was the highest test score?

How many students were in the class?

What was the most common test score?

What percentage of people scored 6 in their test?(L2)

Bar Chart

Question 1

What was the most common fruit?

How much fruit was sold in total?

What percentage of people bought oranges?
(L2)

Question 2

What was the most common sport?

How many people were surveyed?

What percentage of people prefer basketball?
(L2)

Key Facts– Recap

Write down 5 key facts about Line Plots / Bar Charts:(L2)

1)

2)

3)

4)

5)

Restaurant
Tally
Frequency

Line Plots / Bar Charts

Question 1

What is your favourite Restaurant?

a)Represent above information on a Line Plot and a Bar Chart.(L2)

Line Plot / Bar Chart

b) What fraction of students chose ______as their favourite restaurant?

c) What is the modal restaurant?

d) What percentage of students prefer ______?(L2)

Question 2

Film
Tally
Frequency

What is your favourite film?

a)Represent above information on a Line Plot and a Bar Chart.(L2)

Line Plot / Bar Chart

b) What fraction of students like ______?

c) What is the modal film?

d) What percentage of students like ______?(L2)

Surveys

Types of Data:

Primary Data is data which you collect yourself.

Secondary Data is data you find in newpapers, books or online.

Survey

A Survey is a way of finding information from people for a particular purpose. It involves
- asking questions
- recording what people say
- presenting information in a way that makes it easy to understand.

Example: Companies ask customers to complete questionnaires to find ways in which they can improve the service they offer.

Planning a Survey - Key information:

Population – Entire Group / Sample – A group from the population

You have to know exactly what you need to find out.

Give simple and clear questions to avoid any confusion

Avoid asking personal questions

Don’t ask too many questions

How to collect the data (over the phone, interview, questionnaire (online, postal), etc…)

Questionnaires - Key points:

Questions should be clear, short and easily understood.

Start with simple questions to encourage the person who is completing the questionnaire.

Avoid leading questions. These are questions that suggest a particular response.

Avoid personal questions.

Activity – In your exercise books
In pairs, make a survey based on a specific topic:
You must create 10 questions (5 numerical questions / 5 categorical questions)
Al surveys will be read out at the end of the lesson.

Additional Questions(L3)

Question 1 - A group of drivers were asked how many attempts they had taken to pass their driving test. The results are shown in the following table:

Number of attempts / 1 / 2 / 3 / 4
Number of people / 9 / 13 / 6 / 2

a)Draw a line plot to display the results. Hence calculate how many people were surveyed?

Question 2 - Twenty teachers were asked to match the following songs with the following artists:

Song / Artist
‘Meet me half way’ / Lady Gaga
‘The Climb’ / Kings of Leon
‘Bad Romance’ / Beyonce
‘Use somebody’ / Miley Cyrus
‘Halo’ / Black Eyed Peas

The results are shown below:

Number of matches / 0 / 1 / 2 / 3 / 4 / 5
Frequency / 4 / 3 / 5 / 2 / 2 / 4

a)Display the results on a bar chart

Pie Charts

Question 1

The Pie Chart shows the results of 50
students favourite activities.
Use the results to answer the following
questions:

How many students chose swimming
as there favourite activity?

What is the modal activity?

Find the angle in the sector representing ‘Golf’.(L2)

Question 2

The Pie Chart shows the results of 36
students favourite types of meet.
Use the results to answer the following
questions:

How many students named Beef as there
favourite type of meet?

How many students are vegetarians?

What is the modal meet?

Constructing Pie Charts(L2)

Question 1

What is your favourite dinner?

Dinner
Tally
Frequency

a)Represent above information on a Pie Chart.

b)What is the modal type of dinner?

c)What percentage of students prefer ______?(L2)

Sport
Tally
Frequency

Question 2

What is your favourite sport?

a)Represent above information on a Pie Chart.

b)What fraction of students chose ______as their favourite sport ?

c)What is the modal sport?

Favourite Subject(L2)

45 students in Amity secondary school were asked what their favourite subject was. The results are shown below:

Subject / Maths / Music / English / P.E. / Art
No. of Students / 15 / 12 / 3 / 9 / 6
Percentage

a)Represent above information on a Pie Chart.

b) What is the modal subject?

Histograms

Histograms are used to show continuous data with equal intervals.

What type of data is this?

Question 1

The histogram shows the length of time it
took a number of children to complete a
maths puzzle.

a) How many children completed this maths
puzzle?

b) What fraction of children complete the
puzzle in less than 10 minutes?

c) What percentage of children took at least 20 minutes to complete the puzzle?(L2)

Question 1

Complete the Tower of Hanoi as quick as you can and keep track time taken.

Time Taken / 0-30s / 30-60s / 60-90s / 90-120s / 120-150s / 150-180s
Tally
Frequency

Draw a histogram to represent the data.

Answer the following questions based on your graph:

(i)Write down the modal time.

(ii)Where does the median lie?(L3)

(iii)What percentage of people took less than 1.5 minutes.

Question 2

Below are the results from a Maths Test:

Percentages / 0-20 / 20-40 / 40-60 / 60-80 / 80-100
Frequency / 3 / 10 / 15 / 8 / 9

Represent the above information on a Histogram.

a)How many students completed the maths assessment?

b)What is the modal percentage?

c)What percentage of students scored below 40%?

*Calculate the mean using grouped frequency – in exercise books. (L3)

Shape of a Distribution (L3)

Stem & Leaf Diagram Worksheet

Question 1

The stem & leaf diagram below shows the ages, in years, of 25 people who wished to enter a 10 km walking competition.

a)How many people completed the race?

b)How many people were less than 20 years old?

c)Write down the modal age.

d)How many people were between 25 and 35 years old?

e)What was the median age?(L3)

Question 2

The stem and leaf plot shows the
height, in centimeters, of 22 women
at a gym.

a)What is the range of the heights
of the woman?

b)How many women are more
than 170cm?

c)How many women are between
150cm and 160cm, inclusive?

d)What is the mean height? (L3)

Game of Greed:

Everyone stands. I will throw the two die and total the numbers. This is everybodys current score. Those that are happy with that score sit down and record that score as they are finished with that round. For the others that are still standing, the die is rolled again.

If the die is 1,3,4,5 or 6 that number is added to their past total. If it is a 3, the game is over and all those still standing receive a 0 for that round.

A game consists of 5 rounds. The total game score is the sum of the 5 rounds.

Round 1: / Round 2: / Round 3:
Round 4: / Round 5: / Total:

Student data:

Represent the above information on a Stem & Leaf Diagram.

(L3)

Separate the scores of the male and female students in the class. Represent this information on a back-to-back stem & leaf diagram:

Calculate the mean, mode, median and range of both sets of data.(L3)

Male / Female
Mean
Mode
Median
Range

Are these results a true reflection of the data?

Question 3

The data below shows the ages of 20 employees in a business.

19172633314141272528

40312929392636263538

a)Construct a stem and leaf diagram to represent these ages.

b)What is the modal age?

c)What is the range of the data?

d)What percentage of the employees were 25 years of age or younger?

e)What is the median age?(L3)

f)What is the mean age?(L3)

Question 4

The data below shows the grades of 15 students

9143778355

6396617270

5545925081

a)Construct a stem and leaf diagram to represent these test scores.

b)What is the modal score?

c)What is the range of the data?

d)What percentage of the students scored higher than 80 percent?

e)What is the median score?(L3)

f)What is the mean score?(L3)

Back-to-back Stem & Leaf Diagram (L3)

Height v Arm Span:

Height
Arm Span

Represent the above information on a back-to-back stem & leaf diagram:

Calculate the mean, mode, median and range of both sets of data.(L3)

Height / Arm Span
Mean
Mode
Median
Range

What conclusions can be drawn from the data?(L3)

Interquartile Range(L3)

Step 1: Arrange data in order of size

Step 2: Lower Quartile (Q1) is the value one quarter of the way into data

Step 3: Upper Quartile (Q3) is the value three quarters of the way into data

Step 4: Interquartile Range = Upper (Q3) – Lower (Q1)

Question 1

These are the test marks of 11 students:
52, 78, 61, 49, 79, 47, 54, 58, 72, 62, 73

Write in order:

Calculate the Lower Quartile (Q1)

Calculate the Upper Quartile (Q3)

Calculate the Interquartile Range (Q3 – Q1)

Question 2

These are the times for 16 runners to complete 5km race:

15, 22, 28, 19, 21, 17, 30, 28, 16, 20, 27, 23, 14, 17, 25, 29

Write in order:

Calculate the Interquartile Range (Q3 – Q1)

1